Evidence for a Functional Proximity Law in Multilayer Networks

Vladi Ivanov's paper 'Evidence for a Functional Proximity Law in Multilayer Networks' introduces a new principle: hub importance scores persist more strongly between functionally similar layers than dissimilar ones. This Functional Proximity Law was tested across 17 pre-registered experiments covering 12 canonical domains (molecular biology, neuroscience, computer systems, ecology, linguistics) plus 5 external validations on independently-authored datasets. Eight canonical domains reached p < 0.05 individually, and the directional inequality held in all 9 confirmed cases. Three domains were denied, revealing named structural boundary conditions that narrow the law's scope.

A fully external validation on the C. elegans connectome (independent data and layer definitions) yielded r = 0.777 (p = 0.004). The binomial probability of 14/17 pre-registered confirmations by chance is p ~ 0.006. The law is falsifiable, makes testable directional predictions, and identifies the structural conditions under which it fails. This work has implications for understanding information flow, resilience, and dynamics in complex systems ranging from biological networks to digital infrastructure.